1. LTE Course for Technical Personnel
Summer School ATHENA 2011
LTE
Air Interface

2. History - Details
 1G FDMA (NMT, AMPS, TACS) 80’s
- Voice (analog traffic, digital signaling)
 2G TDMA (GSM, D-AMPS, PDC) and CDMA (IS-95) 90’s
- Voice, SMS, CS data transfer ~ 9.6 kbit/s (50 kbit/s HSCSD)
 2.5G TDMA (GPRS) 00’s
- PS data transfer ~ 50 kbit/s
2.75G TDMA (GPRS+EDGE) 00’s
- PS data ~ 150kbit/s
 3-3.5G WCDMA (UMTS) and CDMA 2000 00’s
- PS & CS data transfer ~ 14-42 Mbit/s (HSPA/HSPA+), Voice, SMS
 3.9G OFDMA (LTE/SAE) 10’s
- PS Data and Voice (VoIP) ~ 100Mbit/s
 4G IMT Advanced source

3. 3G Evolution
 HSPA Evolution
– gradually improved performance at a low additional cost prior to
the introduction of LTE
 LTE
– improved performance in a wide range of spectrum allocations
HSUPA
MBMS
Rel 6
MIMO
HOM
CPC
Rel 7Rel 4R99
HSDPA
Rel 5
4G
Further
enhancements
WCDMA/HSPAWCDMA HSPA Evolution
Rel 8
LTE
LTE
Advanced
source

4. R99
LTE
HSPA
evolved
HSPA
Enhanced UplinkHSDPA
3GPP Rel 99/4 Rel 5 Rel 6
WCDMA EvolvedWCDMA
Rel 7 Rel 8
LTE
HSPA Evolved
LTE
HSPA+
3GPP standard evolution
 Initial packet data in Rel 99/Rel 4
 High Speed Downlink Packet Access in Rel 5
 Enhanced Uplink in Rel 6
 ”High Speed Packet Access+” in Rel 7 e.g.:
– Multiple Input Multiple Output (MIMO)
– Higher order modulation DL/UL
 Long Term Evolution in Rel 8
384
kbps
14.4 /
5.8
Mbps
28 /
12
Mbps
>100
Mbps

5. Telephony
WWW
@
Office
TV
MobileHome
Why LTE/SAE ? - Mobile Triple Play
- Telephony, Data and Video/TV
all service delivered by one network

6. LTE – Targets
 High data rates
– Downlink: >100 Mbps
– Uplink: >50 Mbps
– Cell-edge data rates 2-3 x HSPA Rel. 6 (@ 2006)
 Low delay/latency
– User plane RTT: < 10 ms RAN RTT (fewer nodes, shorter TTI)
– Channel set-up: < 100 ms idle-to-active
(fewer nodes, shorter messages, quicker node resp.)
 High spectral efficiency
– Targeting 3 X HSPA Rel. 6 (@ 2006 )
 Spectrum flexibility
– Operation in a wide-range of spectrum allocations, new and existing
– Wide range of Bandwidth: 1.4, 1.6, 3.0/3.2, 5, 10, 15 and 20 MHz, FDD and TDD
 Simplicity – Less signaling, Auto Configuration e-NodeB
– ”PnP”, ”Simple as an Apple”
 Cost-effective migration from current/future 3G systems
 State-of-the-art towards 4G
 Focus on services from the packet-switched domain

7. EPS Architecture
eNB eNB
eNB
MME/S-GW MME/S-GW
S1
X2
X2
X2
SAE
(System Architecture
Evolution)
LTE
(Long Term Evolution)
EPC
(Evolved
Packet Core)
E-UTRAN
EPS
(Evolved
Packet
System)
UE
source

8. source

9. source

10. PCRF
Overall Architecture
X2-UP
S1-UP (User Plane)
EPC
S1-CP (Control Plane)
E-UTRAN
eNodeBeNodeB
S11
MME
S-GW
P-GW
S5/S8
X2-CP
P-CSCF
S7/Gx
Network & Service
management
OSS-RC EMA
MM DNS/ENUM
HSS
S-CSCF
I-CSCF
IMS Control
layer
Platforms / Concepts
TSP/NSP or
TSP/IS
DNS/
ENUM
MGC
MGW
SUN
IS
A-SBG
CPP /
RBS6000
Juniper/
Redback
WPP
GERAN UTRAN
Broadband
Wired Access
GPRS
Packet
Core
SGSN
GGSN
CDMA2000
HRPD
(EV-DO)
WLAN
N-SBG
Internet
S6a
CS Core
MSC
GWMSC
PSTN
PDSN
S1-AP, X2-AP
H.248
ISUP
Diameter
S3
S4
GTP-C
Gxa
S103
S2a
RNC
Other
SIP/UDP or SIP/TCP
Rx+
User data
RTP/UDP GTP/UDP
S101
IMS Connectivity
layer
Service LayerAS
AS AS
Application Servers
MTAS
S6d
Uu
source

11. Typical Implementation of SAE/LTE
- combined SGSN/MME
Iub
3G
(HSPA & DCH)
S1-UP
UTRAN
Node B
Internet
Evolved
Packet
Core
S1-CP
Iu-CP
LTE
Gi
S4/S11
SAE
BTS
Gb
Abis
2G
GERAN
BSC
SGSN/
MME
P/S-GW
RNC
X2-UP
E-UTRAN
eNodeBeNodeB
X2-CP
Gn

12. Multiple Access Approaches
Frequency
Division
Multiple
Access
Each User has a unique
frequency
(1 voice channel per user)
All users transmit at the
same time
AMPS, NMT, TACS
Each Transmitter has a
unique
Scrambling Code
Each Data Channel has a
unique Channelization
code
Many users share the
same frequency and time
IS-95, cdma2000,
WCDMA
Code
Division
Multiple
Access
Spread
Spectrum
Multiple
Access
Each User has a unique
time slot
Each Data Channel has a
unique
position within the time slot
Several users share the
same frequency
IS-136, GSM, PDC
Time
Division
Multiple
Access
Orthogonal
Frequency
Division
Multiple
Access
Each User and each channel
has a unique
Time and Frequency
Resource
Many users are separated in
frequency and/or time
LTE, Wimax
(WLAN 802.11a,g, DAB radio)

13. LTE Physical Layer
 Flexible bandwidth
– Possible to deploy in 6 different bandwidths
up to 20 MHz
 Uplink: SC-FDMA with dynamic bandwidth (Pre-coded OFDM)
– Low PAPR  Higher power efficiency
– Reduced uplink interference (enables intra-cell
orthogonality )
 Downlink: Adaptive OFDM
– Channel-dependent scheduling and link adaptation
in time and frequency domain
 Multi-Antennas, both RBS and terminal
– MIMO, antenna beams, TX- and RX diversity, interference rejection
– High bit rates and high capacity TX RX
frequency
frequency
 Harmonized FDD and TDD concept
– Maximum commonality between FDD and TDD
 Minimum UE capability: BW = 20 MHz
10 15 20 MHz3
fDL
fUL
FDD-only
fDL
fUL
Half-duplex FDD
fDL/UL
TDD-only
Δf=15kHz
180 kHz
User #2 scheduledUser #1 scheduled
User #3
scheduled
1.4 5
source

14. Time-domain
Structure FDD
Normal CP, 7 OFDM
symbols per slot
TCP Tu  66.7 s
#0 #1 #9
One OFDM symbol
One slot (0.5 ms) = 7 OFDM symbols
One subframe (1 ms) = two slots
One radio frame (10 ms) = 10 subframes = 20 slots
#2 #3 #4 #5 #6 #7 #8
•PBCH sent in subframe #0, slot 1, symbol 0-3 over 4 consequtive radio frames (40 ms)
•SCH sent in subframe #0 and #5, slot 0 and 10, symbol 5-6 (4-5 in case of extended CP)
PBCH
S-SCH P-SCH S-SCH P-SCH
frequency
Δf=15kHz
180 kHz
User #2 scheduledUser #1 scheduled
User #3
scheduled
source

15. Segmentation, ARQ
Ciphering
Header Compr.
Hybrid ARQHybrid ARQ
MAC multiplexing
Antenna and
resrouce mapping
Coding + RM
Data modulation
Antenna and
resource mapping
Coding
Modulation
Antenna and
resource
assignment
Modulation
scheme
MACscheduler
Retransmission
control
Priority handling,
payload selection
Payload selection
RLC
#i
PHY
PDCP
#i
User #i User #j
MAC
Concatenation, ARQ
Deciphering
Header Compr.
Hybrid ARQHybrid ARQ
MAC demultiplexing
Antenna and
resrouce mapping
Coding + RM
Data modulation
Antenna and
resource demapping
Decoding
Demodulation
RLC
PHY
PDCP
MAC
eNodeB UE
Redundancy
version
IP packet IP packet
EPS bearers
E-UTRA Radio
Bearers
Logical Channels
Transport Channels
Physical Channels
Radio
interface
structure
source

16. MAC Layer
Segmentation, ARQ
Ciphering
Header Compr.
Hybrid ARQHybrid ARQ
MAC multiplexing
Antenna and
resrouce mapping
Coding + RM
Data modulation
Antenna and
resource mapping
Coding
Modulation
Antenna and
resource
assignment
Modulation
scheme
MACscheduler
Retransmission
control
Priority handling,
payload selection
Payload selection
RLC
#i
PHY
PDCP
#i
User #i
MAC
IP packet
MAC layer for the LTE access can
be compared to the Rel-6 MAC-
hs/MAC-e and covers mainly
similar functionality:
• HARQ,
• priority handling (scheduling),
• transport format selection
• DRX control
source

17. Channel mapping
UL-SCHPCH DL-SCH
PCCH
Logical Channels
“type of information”
(traffic/control)
Transport Channels
“how and with what
characteristics”
(common/shared/mc/bc)
Downlink Uplink
PDSCH
Physical Channels
“bits, symbols,
modulation, radio
frames etc”
MTCH MCCH BCCH DTCH DCCH DTCH DCCH CCCH
PRACH
RACH
CCCH
MCH BCH
PUSCHPBCH PCFICH PUCCH
-CQI
-ACK/NACK
-Sched req.
-Sched TF DL
-Sched grant UL
-Pwr Ctrl cmd
-HARQ info
MIB SIB
PMCH PHICHPDCCH
ACK/NACK
PDCCH
info
Physical Signals
“only L1 info”
RS SRSP-SCH S-SCH RS
-meas for DL sched
-meas for mobility
-coherent demod
-half frame sync
-cell id
-frame sync
-cell id group -coherent demod
-measurements
for UL scheduling
source

18. Tx & Rx physical layer processing
Coding
Scrambling
Modulation
CRC
Decoding
Descrambling
Demodulation
CRC check
Radio Channel
Not shown:
Rate Matching
HARQ
MIMO mapping...
OFDM(IFFT) OFDM(FFT)
Tx Rx

19. Tx Coding
Coding
Scrambling
Modulation
CRC
Decoding
Descrambling
Demodulation
CRC check
Radio Channel
OFDM(IFFT) OFDM(FFT)
Tx Rx

20. CRC Coding – error detection
Cyclic-Redundancy Check (CRC) Coding
– Identifies any corrupted data left
after error correction function in
receiver
– CRC is used for checking BLER
(Block Error Ratio) in the outer loop
power control
Checksum 24 bits
110010110011
Original Data
244 bits
CRC
Generator
Original Data
1001011010..
CRC
Generator
Re-Generated Checksum
110010110001
Transmitter
Receiver
If Checksums do not match,
there is an error
Received Data
1001010010..
Received Checksum
110010110011
RF
Transmission Path
The longer the checksum, the greater is
the accuracy of the process. Why???
Answer:
Various combinations of errors in the data and the
checksum would produce the same checksum. The
longer the checksum the less likely it is for this to
happen.
Example: 24 bits of binary information
represents 16 777 216 (224) different
combinations

21. FEC Coding
 Error Correction
Help the receiver correct bit errors caused by the air interface.
– How do you correct errors at the receiver?
Send
message
many times?
010010110,
010010110,
010010110,
010010110,
010010110,



Forward
Error
Correction!
Up to 6x data expansion...
But the most powerful results
Advantage:
The more times the data is
transmitted the better is the error
protection.
Disadvantage:
However the bandwidth is also
increased proportionally
Need to find a FEC technique with minimum
BW requirements!!

22. FEC Coding Approaches
– Block Codes (Hamming Codes, BCH Codes, Reed-Solomon
Codes)
– Continuous Codes (Convolutional Codes, Turbo Codes)
 Data is processed continuously through FEC generator
 Resulting data stream has built-in redundancy that can
be extracted to correct bit errors.
– LTE uses Turbo codes with rate 1/3 for DL-SCH transmissions.
– Convolutional coding used for BCH
source

23. FEC Coding
Original Data
00011011...
FEC
Generator
FEC Encoded data
1010011100110110...
Original Data
00011011
Viterbi/
Turbo
Decoder
Transmitter
Receiver
RF
Transmission Path
source

24. Tail Biting Convolutional Encoder
D D D DD D
G0 = 133 (octal)
G1 = 171 (octal)
G2 = 165 (octal)
kc
)0(
kd
)1(
kd
)2(
kd
 Constraint length 7
 Coding rate 1/3
source

25. Radio Channel problems -
Multipath Propagation
Coding
Scrambling
Modulation
CRC
Decoding
Descrambling
Demodulation
CRC check
Radio Channel
OFDM(IFFT) OFDM(FFT)
Tx Rx

26. Multipath Propagation
• Up to date cellular systems have used single carrier modulation
schemes almost exclusively.
• LTE uses OFDM rather than single carrier modulation
• single carrier systems face extreme problems with multipath
induced channel distortion
• A measure of multipath distortion is
provided by delay spread  describes
the amount of time delay at the receiver
from a signal traveling from the
transmitter along different paths.

27. Multipath Propagation
 One user’s signal reflects off many objects
 The received signal contains many time-delayed
replicas

28. Multipath Propagation
- and the resulting impulse response
Multipath Propagation gives rise to:
1. InterSymbol Interference (ISI)
2. Fast fading (Rayleigh fading)
source

29. Multipath Propagation
- and the resulting impulse response
Fast fading (Rayleigh fading)
τ0 τ1 τ2 t(μs)
P0
P1
P2
Power
(dB)
Impulse response

30. Multipath Propagation
- and the resulting impulse response
InterSymbol Interference (ISI)
τ0 τ1 τ2 t(μs)
P0
P1
P2
Power
(dB)
P2,τ1
P0,τ0 P1,τ2
Impulse response
Direct signal
Reflected signal
Path delay
difference
ISI

31. Multipath Fading
Direct Signal
Reflected Signal
Combined Signal

32. Path loss and Fast fading
Power
distance
Time between fades is related to
• RF frequency
• Geometry of multipath vectors
• Vehicle speed:
Up to 4 fades/sec per kilometer/hour
path loss
Rayleigh
Deep fade caused by destructive summation
of two or more multipath reflections

33. Block Interleaving
Coding
Scrambling
Modulation
CRC
Decoding
Descrambling
Demodulation
CRC check
Radio Channel
OFDM(IFFT) OFDM(FFT)
Tx Rx

34. Block Interleaving
Time
Amplitude
To
decoder
Original Data Samples
1 2 3 4 5 6 7 8 9
Interleaving
Matrix
1 2 3
4 5 6
7 8 9
Transmitter
Interleaved Data Samples
1 4 7 2 5 8 3 6 9
RF
Transmission Path
Interleaved Data Samples
1 4 7 2 5 8 3 6 9
Errors Clustered
De-
Interleaving
Matrix
1 2 3
4 5 6
7 8 9
De-Interleaved Data Samples
1 2 3 4 5 6 7 8 9
Receiver
Errors Distributed
Solution:
use a block-interleaving technique as shown:
source

35. Scrambling in LTE
Coding
Scrambling
Modulation
CRC
Decoding
Descrambling
Demodulation
CRC check
Radio Channel
OFDM(IFFT) OFDM(FFT)
Tx Rx

36. Interference in LTE
PROBLEM STATEMENT
In LTE, a frequency reuse of 1 will typically be used. This means that
all cells use the same frequency band(s). For UEs close to the cell
border, this will lead to massive interference in both UL and DL.
Solutions
1. In order to reduce this inter cell interference, a cell specific bit-
level scrambling is applied for all transmissions in both UL and
DL.
2. Inter Cell Interference Co-ordination (ICIC). ICIC co-ordinates
the radio resource allocations (scheduling) between neighboring
cells that experience problems

37. Scrambling in LTE
 Cell specific bit-level scrambling used in LTE for all
datastreams in UL and DL
– used in order to achieve interference randomization
between cells
 No frequency planning (freq reuse 1)
– massive inter-cell interference mitigated by scrambling and
interference co-ordination techniques (e.g. ICIC)
 Common scrambling used for cells in
broadcast/multicast service transmissions (MBMS)

38. Modulation
Coding
Scrambling
Modulation
CRC
Decoding
Descrambling
Demodulation
CRC check
Radio Channel
OFDM(IFFT) OFDM(FFT)
Tx Rx

39. Modulation
Next step after channel coding and scrambling is modulation.
Modulation: A process that maps blocks of scrambled bits (bit rate) onto
symbols (symbol rate or baud rate)  Over the air interface we apply
digital modulation techniques; a digital signal modulates an analog carrier
 different symbols correspond to a specific amplitude and/or phase shift
of the carrier wave.
Three different modulation schemes are supported in E-UTRAN;
• QPSK (Quadrature Phase shift keying)
• 16-QAM (16 Quadrature Amplitude Modulation)
• 64-QAM (64 Quadrature Amplitude Modulation)
QPSK is a pure phase modulation  it has constant amplitude,
16-QAM and 64-QAM both uses a combination of phase and amplitude.

40. Modulation
 The sub-carriers are modulated with a certain modulation scheme
– maps the data bits into a carrier phase and amplitude (symbols)
 E-UTRAN user data channels supports QPSK, 16QAM and 64QAM
 16QAM allows for twice the peak data rate compared to QPSK
 64QAM allows for three times the data rate compared to QPSK
 Higher order modulation more sensitive to interference
– Useful mainly in good radio channel conditions
(high C/I, Little or no dispersion, Low speed)
e.g. Close to cell site & Micro/Indoor cells
 BPSK is used for some signaling (PHICH)
2 bits/symbol 4 bits/symbol 6 bits/symbol
64-QAM16-QAMQPSK
1 bit/symbol
BPSK
0
1
00
11
10
01 1111 111111

41. OFDM Principle
 Parallel transmission using a large number of narrowband “sub-carriers”
 “Multi-carrier” transmission
 Implemented with IFFT (Inverse Fast Fourier Transform) at transmitter and FFT at
receiver side
 Uplink uses similar approach, but with precoder to achieve single carrier
properties
f = 15 kHz
20 MHz (example)
S/P
f1
f2
fM

IFFT
Coded and
modulated
data split
f1
f2
fM
filter
FFT
Tx Rx
P/S
source

42. Background
 OFDM – Orthogonal Frequency Division Multiplex
– a modulation scheme, not a multiple-access scheme
 Basic principle known since the 50’s
– Kineplex system by Collins, …
 Popular/feasible with the ‘discovery’ of FFT in 1965 and
its efficient implementation in HW
– Bell Labs, 1971, implementation through FFT
– Used by LTE, DAB, DVB, WiMax, xDSL, …

43. Orthogonal Frequency Division Multiplexing
Principles
Benefits
+ Frequency diversity
+ Robust against ISI
+ Easy to implement
+ Flexible BW
+ Suitable for MIMO
+ Classic technology
(WLAN, ADSL etc)
Drawbacks
- Sensitive to Doppler
and freq. errors
- High PAPR (not
suitable for uplink)
- Overhead
• Orthogonal: all other subcarriers zero at sampling point
• Delay spread << Symbol time < Coherence time
• Tu – symbol time per subcarrier -> Subcarrier spacing f = 1/Tu
f
source
See next slides

44. Orthogonal Frequency Division Multiplexing
Principles
Coherence time - Physics
coherence time in electromagneti wave theory is the time
over which a propagating wave may be considered coherent.
it is the time interval within which its phase is, on average,
predictable.
Coherence time is related to the classical uncertainty principle
and it relates the bandwidth (spread in frequency)
of signal or wave to its temporal extent df = 1/dt Thus
phenomena with long coherence times will be sharply peaking
with respect to their spectrum, i.e., they will be composed of
less frequencies.
The limit of this is an infinite coherence time, which would
mean the signal is composed of a singular frequency

45. Orthogonal Frequency Division Multiplexing
Principles
Coherence time - Physics
Waves of different frequencies interfere
to form a pulse if they are coherent
Spectrally incoherent waves
interferes to form continuous wave
with a randomly varying phase and
amplitude

46. Orthogonal Frequency Division Multiplexing
Principles
Coherence time - Telecom
In communications systems, a communication channel may
change with time  Coherence time is the time duration over
which the channel impulse response is considered to be not
varying.
Important: Such channel variation is much more significant in
wireless communications systems, due to doppler effects.

47. Orthogonal Frequency Division Multiplexing
Principles
1 11( ) ( ) ( )t ty t x t t h t  
1
( )th t
2 22( ) ( ) ( )t ty t x t t h t  
Coherence time - EXAMPLE
simple model
a signal x(t) transmitted at time t1 will be received as:
Where is the channel impulse response (CIR) at time t1
A signal transmitted at time t2 will be received as
Now, if is relatively small, the channel may be
considered constant within the interval t1 to t2.
Coherence time (Tc) will therefore be given by
And from Clark’s model
2 1
( ) ( )t th t h t
2 1cT t t 
0,423
c
d
T
f


48. OFDM multicarrier transmission
 Single carrier transmission
– each user transmits and receives data stream with only one carrier at
any time
 Multicarrier transmission
– a user can employ a number of carriers to transmit data
simultaneously
– FFT to replace the banks of sinusoidal generators
IFFT
1cos(2 )f t
2cos(2 )f t
cos(2 )Nf t
( )s t

( )s t
S/P
bk
  


N
k
tfj
k
k
ebtx
1
2
  



N
k
ftkj
kebtx
1
2
x(t) x(t)
x1(t)
x2(t)
xN(t)
tfj
e 12
tfj
e 22
tfj N
e 2
source

49. Fourier transform
)]([)()( 2
txFdtetxfX ftj
 



  fxFdfefXtx ftj 12
)()( 


  

 
 f
f
f
ee
fj
dtetdtettF
fjfj
ftjftj
sinc
)sin(
2
1
)()()]([ 2
1
2
1
22
















 Periodic and non-periodic signals, continuous spectrum
 Example for rectangular pulse shape:
source

50. OFDM Transmission
freq
=
freq
*
freq
t

51. OFDM Transmission
freq
freqtime
freq
time

52. -10 -5 0 5 10
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
OFDM Transmission
1subcarrier f
2subcarrier f
3subcarrier f
4subcarrier f
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-10 -5 0 5 10
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-10 -5 0 5 10
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-10 -5 0 5 10
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-10 -5 0 5 10
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
-1.5
-1
-0.5
0
0.5
1
1.5
2
-10 -5 0 5 10
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-10 -5 0 5 10
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
-2
-1
0
1
2
3
4
-10 -5 0 5 10
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Time domain Frequency domain

53. Discrete Fourier Transform (DFT)
 N-point DFT:
 N-point IDFT:
 Discrete sequence of sampled signal, discrete spectrum
 Four-point DFT: multiplying with {1, -1, j, -j}
   
21
0
nkN j
N
n
X k x n e
 

 
   
21
0
nkN j
N
k
x n X k e


 
0x
1x
2x
3x
0X
1X
2X
3X
j
j
1
j
1
1
j
1
0X
1X
2X
3X
0x
1x
2x
3x
 Fast Fourier Transform: FFT
 Derived to “radix-4 algorithm”
 N-point DFT
– N2 multiplications or phase
rotation
– N2 complex additions
 FFT
multiplications
additions
 2
3
log 2
8
N N
 
 
 
2logN N
source

54. Orthogonality
Time domain Frequency domain
Example of four subcarriers within one OFDM symbol Spectra of individual subcarriers
*
1 2( ) ( ) 0x t x t dt



*
1 2( ) ( ) 0X f X f df



source

55. Orthogonal Frequency Division Multiplexing
 Receiver integrates for symbol integral
 Orthogonality criteria:
     
    fTj
T
tffj
T
tfjtfj
T
e
fT
fT
dte
dteedttxtx k












2
0
2
0
*22
0
*
2112
sin21
1
   





1
0
1
0
2
N
k
k
N
k
tfj
k txebtx k
if , n is a non-zero integer, i.e. , thenfT n 
n
f
T
  12 0 
source

56. OFDM and Multicarrier Transmission
(A)
(E)
(D)
(C)
(B)
1cf f 2cf f 3cf f 4cf f 5cf f
1
T
1
T
Orthogonal
Non-orthogonal
Orthogonal, n=3
Orthogonal, n=2
Orthogonal, n=1
(OFDM)
source

57. Guard time and Cyclic Prefix
Direct path:
Reflected path:
Integration interval
 We rely on that the subcarriers are orthogonal
 Short subcarrier spacing (f=15 kHz)  long symbol duration
 Intersymbol interference is eliminated almost completely by introducing a
guard interval with zero padding in every OFDM symbol.
Direct path:
Reflected path:
Integration interval

58. FFT-based OFDM System
Serial-to-
Parallel
Converter
Signal
Mapper
IFFT
Parallel-
to-Serial
Converter
Guard
Interval
Insertion
Serial
Data
Input
x bits
0d
1d
1nd
0s
1s
1ns
D/A &
Low pass
Filter
Up-
Converter
Down-
Converter
A/D
Guard
Interval
Removal
Serial-to-
Parallel
Converter
FFT
One-tap
Equalizer
Signal
Demapper
Parallel-
to-Serial
Converter
Serial
Data
Output
0
ˆdx bits
1
ˆd
1
ˆ
nd
0
ˆs
1
ˆs
1
ˆ ns
Channel
)(ts
Time
Frequency
Subchannels
Fast Fourier
Transform
Guard
Intervals
Symbols
source

59. Links and references
www.3gpp.org
 Evolved Universal Terrestrial Radio Access (E-UTRA) and Evolved Universal Terrestrial
Radio Access (E-UTRAN); Overall description; Stage 2, 36.300
 Evolved Universal Terrestrial Radio Access (E-UTRA); Physical Channels and Modulation,
36.211
 Evolved Universal Terrestrial Radio Access (E-UTRA); Multiplexing and channel coding ,
36.212
 Evolved Universal Terrestrial Radio Access (E-UTRA); Physical layer procedures, 36.213
 Evolved Universal Terrestrial Radio Access (E-UTRA); Physical layer; Measurements ,
36.214
 LTE Physical Layer – General Description, 36.201
A good book:
 3G Evolution – HSPA and LTE for Mobile Broadband, Academic Press 2007
Erik Dahlman; Stefan Parkvall; Johan Sköld; Per Beming

60. 36.201 – Physical layer general description
36.211 – Physical channels and modulation
36.212 – Multiplexing and channel coding
36.213 – Physical layer procedures
36.214 – Physical layer measurements
36.300 – E-UTRA overall description
36.302 – Services provided by the physical layer
36.304 – UE Functions related to idle mode
36.306 – UE radio access capabilities
36.321 – Medium Access Control (MAC)
Protocol Specification
36.322 – Radio Link Control (RLC)
Protocol Specification
36.323 – Packet Data convergence Protocol (PDCP)
Protocol Specification
36.331 – Radio Resource Control (RRC)
Protocol Specification
36.101 – UE radio transmission and reception (FDD)
36.104 – BTS radio transmission and reception (FDD)
36.113 – Base station EMC
36.133 – Requirements for support of Radio Resource
Management (FDD)
36.141 – Base station conformance testing (FDD)
36.401 – E-UTRA Architecture Description
36.410 – S1 interface general aspects & principle
36.411 – S1 interface Layer 1
36.412 – S1 interface signalling transport
36.413 – S1 application protocol S1AP
36.414 – S1 interface data transport
36.420 – X2 interface general aspects and principles
36.421 – X2 interface layer1
36.422 – X2 interface signalling transport
36.423 – X2 interface application part X2AP
36.442 – UTRAN Implementation Specific O&M Transport
All specifications can be found on the
web site www.3gpp.org
LTE Specifications
23.002 – Network Architecture
23.003 – Numbering, addressing and identification
23.009 – Handover Procedures
23.048 – Security mechanisms for USIM application
23.401 – GPRS enhancements for eUTRA
23.907 – QoS Concept
24.301 – NAS Protocol for Evolved Packet System (EPS)
24.302 – Access to the EPC via non 3GPP networks
33.401 – System Architecture Evolution (SAE);
Security Architecture

61. Links and references